the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Electrical conductivity fluctuations as a tracer to determine time-dependent transport characteristics in hyporheic sediments
Jonas Leon Schaper
Olaf A. Cirpka
Joerg Lewandowski
Christiane Zarfl
Abstract. Assessing water transport in riverbed sediments is important for quantifying the effective reactivity of hyporheic sediments and the magnitude of groundwater-surface water exchange flows. A typical approach of estimating transport in riverbed sediments is by measuring natural tracers such as heat or electrical conductivity (EC) and fitting models to them that assume time-independent travel time distributions, implying steady-state flow. Here, we use a transport parameterization that is based on the advection-dispersion equation (ADE) with coefficients that continuously vary in time. The ADE is solved numerically and its solution is fitted to measured EC time series using Bayesian parameter inference. A continuous function of model parameters is constructed by smoothly interpolating between point values with different temporal resolution, and Tikhonov regularization is used to avoid spurious parameter fluctuations. The approach is tested using EC time series synchronously measured in surface water and hyporheic porewater of two urban rivers in Germany and one urban river in South Australia. For all datasets the goodness of fit was improved by introducing a time-dependent EC offset. Estimated porewater velocities were highly transient in three out of the four datasets with values increasing by a factor of 6 over the course of 24 h and were likely related to both variations of hydraulic gradients along and spatial shifting of flow paths. Non-parametric deconvolution indicated that transport in three out of four datasets could be characterized as Fickian, but that flux transients may induce multimodality in stationary travel time distributions. Given the high temporal dynamics, transport characteristics encountered in the streambed sediments of the three investigated urban rivers, we envision that the presented model is a valuable tool to improve the accuracy of both reactive transport simulations and assessments of biogeochemical turnover in riverbed sediments.
- Preprint
(1279 KB) - Metadata XML
-
Supplement
(4038 KB) - BibTeX
- EndNote
Jonas Leon Schaper et al.
Status: final response (author comments only)
-
RC1: 'Comment on hess-2023-141', Anonymous Referee #1, 28 Aug 2023
The study utilizes electrical conductivity (EC) as a natural tracer to evaluate water transport in the hyporheic zones of urban rivers in Germany and South Australia. By employing a time-dependent advection-dispersion equation (ADE) fitted to EC time series through Bayesian parameter inference, the research demonstrates that porewater velocities are highly variable, experiencing up to a six-fold increase within a 24-hour period. The study purports to validate the Fickian nature of transport in three out of four datasets, thereby affirming the applicability of ADE-based models. However, it recommends caution in interpreting Travel Time Distributions (TTDs) derived from EC, particularly when these distributions display tailings and multiple secondary peaks. The work is well-suited for HESS, and both the modeling and dataset are relevant to the community.
The paper's primary issue lies in the lack of clarity in its presentation and the insufficient contextualization of the work. Regarding clarity, the derivation and presentation of the model are inadequate. Specifically, it is challenging to comprehend the rationale behind various aspects involving the time series data, such as: why are EC measurements offset only once a day? Why choose 1-8 velocity values per day instead of a continuous velocity change? How are the weight values determined? Is it merely by visually inspecting the ratio from the L curves? What constitutes a hypothetical flow line? Additional examples will be presented later. Furthermore, the frequent references to figures and tables in the supplementary material necessitate constant toggling between the supplementary material and the main paper, suggesting that these should be integrated into the main paper.
In terms of context, the authors seem to overlook a substantial body of literature on anomalous transport in the hyporheic zone. This omission is surprising, especially considering that one dataset in their study is non-Fickian. Moreover, the complex processes involved in setting daily velocity values, and extracting weighting times from a hypothetical flow line could potentially result in overfitting the data to appear as Fickian flow. Therefore, I recommend exploring and acknowledging other non-Fickian possibilities and referring to the extensive non-Fickian literature in the hyporheic zone. A few select references are provided, but there are many more:
Singha, Kamini, et al. "Electrical characterization of non‐Fickian transport in groundwater and hyporheic systems." Water Resources Research 44.4 (2008).
Boano, Fulvio, et al. "A continuous time random walk approach to the stream transport of solutes." Water Resources Research 43.10 (2007).
Roche, Kevin R., et al. "Effects of turbulent hyporheic mixing on reach‐scale transport." Water Resources Research 55.5 (2019): 3780-3795.
Berkowitz, Brian, and Erwin Zehe. "Surface water and groundwater: unifying conceptualization and quantification of the two “water worlds”." Hydrology and Earth System Sciences 24.4 (2020): 1831-1858.
Drummond, J. D., et al. "Effects of solute breakthrough curve tail truncation on residence time estimates: A synthesis of solute tracer injection studies." Journal of Geophysical Research: Biogeosciences 117.G3 (2012).
Sherman, Thomas, et al. "A dual domain stochastic lagrangian model for predicting transport in open channels with hyporheic exchange." Advances in water resources 125 (2019): 57-67.
Haggerty, R., Wondzell, S. M., and Johnson, M. A.: Power-law residence time distribution in the hyporheic zone of a 2nd-order mountain stream, Geophys. Res. Lett., 29, 18-1–18-4, (2002).
Detailed comments:
Line 143: The sentences, "Thus, we use equation 1 only as a parameterization to obtain time-dependent transfer functions, and we consider the coefficients determined upon calibration as apparent ones. In particular, the time variable velocity may in reality reflect effects of both changes in the true porewater velocities and shifts in travel paths," are unclear. If the ADE is merely used to parameterize the coefficients, how can the study claim the flow is Fickian? This appears tautological. Clarification is needed on why this procedure and the associated ADE are superior to other methods.
Furthermore, the authors repeatedly mention throughout the manuscript that travel paths may shift, but they do not elucidate the mechanism responsible for these changes in flow paths. This is crucial, as understanding the mechanism could constrain the variations in flow paths in alignment with the proposed model.
Line 152: What is the rationale for having only one EC offset per day? Given the data for the stream stage, there could be two offsets per day or a common trend line. An explanation for this choice is needed.
Line 155: Similarly, why decide on 1, 2, 4, and 8 velocity values per day? Is there a marker in the data that suggests this? Are there known changes in the head value that necessitate this range of change?
Line 159: It is assumed that bold font indicates a vector for all variables, yet this is not explicitly stated in the text.
Line 166: The sentence, "subject to a constant that does not depend on the parameters," is unclear. What does this mean in the context of the study?
Paragraph 174-181: While the method of finding weights through L-curves is described, the reason for doing so is not clear. What purpose does the weighting serve? Is it only to establish how well the model captures the measurements? If so, why is it just “an additional measure of the goodness of fit”?
Line 184: How is the hypothetical flow line established? Given that velocity seems to be unknown due to the unknown path, how many possibilities are there?
Line 201: The paper is laden with specialized jargon that, in my opinion, detracts from its accessibility. For instance, the term "homoscedastic epistemic model error" could be simplified. "Homoscedastic" could be replaced with "homogeneity of variances," and "epistemic" could be substituted with "model uncertainty," resulting in the phrase "variance homogeneity uncertainty due to measurement errors." My potential misinterpretation of these terms underscores the need for clearer explanations rather than reliance on specialized jargon, especially given the broad readership of HESS. I recommend clarifying the terminology to make the paper more accessible to a wider audience.
Line 266-270: The authors transparently enumerate all potential processes that could influence the EC measurements and introduce errors, which is commendable. However, they do not specify how they address these issues. Is this accounted for in the "homoscedastic epistemic model error"? Is there a methodology to estimate the impact of each process relative to the measurement? In line 279, they state that all these ranges of uncertainty should be considered as model uncertainties. Yet, there are distinct approaches to handling model uncertainties (via ensemble methods) and measurement uncertainties (by calculating the potential range of influence). While the authors do acknowledge this by discussing the correlation between coefficients, they conclude by stating, "It is thus likely that the temporal dynamics of EC offset are predominantly related to measurement error." If so, why substitute one form of uncertainty for another when they stem from different sources? This is particularly perplexing given that changes in flow paths are consistently cited as the reason for broad peaks in travel-time distribution and other discrepancies, yet this form of uncertainty is not addressed in the study.
Figure 2: Why is there a discrepancy between the "measured" velocity peak and the mean advective travel time peak? It appears that the maximal residence peaks are misaligned with the corresponding porewater velocity, which is perplexing since one is a consequence of the other.
Figure SI-1: Should there be a variation in the dimensions of the regularization weights for porewater velocity (), and the EC offset dimension, ()?
The term "Stream stage" is frequently mentioned but not defined. This is a recurring issue in the paper and is often the result of using specialized jargon in papers aimed at a specific audience. Please define all terms and refrain from using specialized terminology where possible.
In summary, while this paper has the potential for publication in HESS, it currently suffers from a lack of clarity and is filled with unnecessary jargon. Furthermore, the model's assumptions and key stages are not well-explained. The paper also needs to be situated within the context of existing literature, particularly given the extensive body of work that suggests alternative viewpoints.
Citation: https://doi.org/10.5194/hess-2023-141-RC1 -
RC2: 'Comment on hess-2023-141', Anonymous Referee #2, 09 Sep 2023
This MS concerns the inverse problem of inference of point-to-point transfer functions for short travel distances beneath streambeds. Although some calibrated hyporheic flow time series are presented and a few remarks made concerning the nature of the transport uncovered, this is not the focus of the paper. This is presented as a paper introducing a new calibration method, and I am considering it primarily on that basis.
I found the presentation confusing and it difficult to determine just what was being proposed, based the information provided in the manuscript. This is obviously a major problem in a document aiming to outline a new method. In particular, it is not at all clear what the relationship is between Equations (4) and (8). Many times, reference is made to use of the non-parametric deconvolution algorithm of Cirpka (2007), and (8) is naturally applicable without specifying a functional form of g(). But elsewhere there is reference to whether transport is or is not Fickian, and to the underlying dispersivity and velocity, as shown in (1). This of course implies a parametric calibration. The two formulations differ in their interpretation of the primary source of mismatch (measurement vs. model error), and in what time series' quadratic variations they penalize (latent variables vs. outcome). Surprisingly to me, the non-parametric (8) appears to be used in a context where the realism and physical interpretation of the underlying parameters are of interest: where the Fickian or non-Fickian nature of the transfer functions is concerned. It seems like it would be ideal to identify the best-fit Fickian transfer function via (4) and compare it with the empirical result.
I am also concerned about the introduction of the physically unmotivated "offset" o(t) that fudges the difference between the EC predicted by the transient ADE and the observed EC, and which is allowed to change every day. It is not clear why this function is needed at all. It is possible to simply find the best-fitting calibrated model against a time series by a least squares plus penalty functional procedure similar to the ones shown in the paper. It appears o(t) might have been introduced so that part of the mismatch can be categorized as measurement error in (4). I generally expect model error to dwarf measurement error in these sorts of applications, and in any event, a coarse temporal resolution of o(t) is considered, so the first term of (4) inherently contains some model error. And furthermore, the two regularization terms in (4) do not have a probabilistic foundation: they are determined from the L-curve approach, which is rooted in the idea of minimum MSE. It seems like the complexity of o(t) can be dispensed with from the point of view of parameter identification.
I believe the authors should demonstrate the superiority of the calibration approach in (4) relative to a straightforward approach that does not include the offset and/or time-varying velocity by computing AICc. Furthermore, it is not clearly shown how well the model (1) fits the data, and how much work o(t) is doing to fudge the difference between model prediction and observed data, and how much it is being allowed to vary, ad hoc, from day to day. This should be shown.
Figure 3b appears to show a comparison of measured and simulated time series, but there is a very obvious delay visible between the two time series. Why did this not result in a differently identified velocity?
Statements about the seemingly Fickian / non-Fickian nature of the travel time distributions seem to be based on eyeballing the non-parametric distributions shown in Figure 4. In my view, there is not enough evidence given to support these statements.
Finally, it would be helpful for the authors to highlight the novelty in the presented results. The model-free deconvolution approach is previously published, and other major aspects---Bayesian framing, quadratic penalty functional, use of L-curve to trade off bias and variance---are all well established in the literature. Is the particular way they are combined original? (Again, this is hard to evaluate because of the confusing presentation.) Or is it the use of these classic techniques in the context of hyporheic flow that is new? Whatever the claim to originality, it should be made clear and contextualized relative to existing literature.
Citation: https://doi.org/10.5194/hess-2023-141-RC2 -
RC3: 'Comment on hess-2023-141', Anonymous Referee #3, 25 Sep 2023
As the earlier reviewers state, the article concerns an interesting and relevant topic but is full with what seem to be arbitrary choices and ad hoc solutions. Something like the time-varying EC off-set, o(t), is such an artefact. No serious physical explanation is provided. To keep things from pure noise-fitting, a regularization is applied but the choice of the weights is based on visual inspection, which is difficult to replicate.
The reason to accept a Fickian model seems to be necessary but not sufficient. What would be the results if non-Fickian models were applied throughout?
Why is maximum likelihood used for sigma_ep and expectation maximization for Theta? And so forth.
It would probably be difficult to go through everything in such detail that the reader becomes convinced of the reasonableness of it all, also because a lot has been covered in an earlier article by Cirpka. A possible way forward is to accompany the article by something like a Python Notebook with annotated code and prepped data sets. That would allow readers to get a better idea about the visual inspection of the steepness of the L-curve, etc. Presently, the code is available on request, which is a good step but it could be better and the impact of the article would be much stronger.
Citation: https://doi.org/10.5194/hess-2023-141-RC3
Jonas Leon Schaper et al.
Jonas Leon Schaper et al.
Viewed
| HTML | XML | Total | Supplement | BibTeX | EndNote | |
|---|---|---|---|---|---|---|
| 317 | 67 | 10 | 394 | 26 | 4 | 8 |
- HTML: 317
- PDF: 67
- XML: 10
- Total: 394
- Supplement: 26
- BibTeX: 4
- EndNote: 8
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1